General-purpose parallel computing architecture

ABSTRACT

An apparatus includes multiple computing cores, where each computing core is configured to perform one or more processing operations and generate input data. The apparatus also includes multiple coprocessors associated with each computing core, where each coprocessor is configured to receive the input data from at least one of the computing cores, process the input data, and generate output data. The apparatus further includes multiple reducer circuits, where each reducer circuit is configured to receive the output data from each of the coprocessors of an associated computing core, apply one or more functions to the output data, and provide one or more results to the associated computing core. In addition, the apparatus includes multiple communication links communicatively coupling the computing cores and the coprocessors associated with the computing cores.

CROSS-REFERENCE TO RELATED APPLICATIONS AND PRIORITY CLAIM

This application claims priority as a continuation-in-part of U.S. patent application Ser. No. 15/439,777 filed on Feb. 22, 2017, which is a continuation-in-part of U.S. patent application Ser. No. 15/157,218 filed on May 17, 2016, which claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 62/165,052 filed on May 21, 2015 and U.S. Provisional Patent Application No. 62/173,866 filed on Jun. 10, 2015. All of these applications are hereby incorporated by reference in their entirety.

TECHNICAL FIELD

This disclosure relates generally to hardware architectures for computing devices and computing systems. More specifically, this disclosure relates to a general-purpose parallel computing architecture, which can support advanced computing functions such as those used in artificial intelligence.

BACKGROUND

The human brain is a massively parallel system typically containing around 100 billion neurons connected by one quadrillion synapses. Ideally, simulating the operation of the human brain could support advanced computing functions such as artificial intelligence. However, conventional attempts at simulating the human brain or designing computing systems that rival the abilities of the human brain have generally been inadequate for a number of reasons, such as not substantially matching the connectivity or three-dimensional structure of the brain.

SUMMARY

This disclosure provides a general-purpose parallel computing architecture.

In a first embodiment, an apparatus includes multiple computing cores, where each computing core is configured to perform one or more processing operations and generate input data. The apparatus also includes multiple coprocessors associated with each computing core, where each coprocessor is configured to receive the input data from at least one of the computing cores, process the input data, and generate output data. The apparatus further includes multiple reducer circuits, where each reducer circuit is configured to receive the output data from each of the coprocessors of an associated computing core, apply one or more functions to the output data, and provide one or more results to the associated computing core. In addition, the apparatus includes multiple communication links communicatively coupling the computing cores and the coprocessors associated with the computing cores.

In a second embodiment, an apparatus includes multiple computing cores, where each computing core is configured to perform one or more processing operations and generate input data. The apparatus also includes multiple coprocessors associated with each computing core, where each coprocessor is configured to receive the input data from at least one of the computing cores, process the input data, and generate output data. The apparatus further includes multiple communication links communicatively coupling the computing cores and the coprocessors associated with the computing cores. The coprocessors in a subset of the coprocessors for each computing core are also configured to collectively apply one or more functions to the output data, where one of the coprocessors in the subset is further configured to provide one or more results to the associated computing core.

In a third embodiment, an apparatus includes N parallel computing cores, where each computing core is configured to perform one or more processing operations and generate input data. The apparatus also includes N×N coprocessors, where each computing core is associated with N parallel coprocessors. Each coprocessor is configured to receive the input data from at least one of the computing cores, process the input data, and generate output data. The apparatus further includes N reducer circuits, where each computing core is associated with one of the reducer circuits. Each reducer circuit is configured to receive the output data from each of the coprocessors of the associated computing core, apply one or more functions to the output data, and provide one or more results to the associated computing core. In addition, the apparatus includes multiple communication links communicatively coupling the computing cores and the coprocessors associated with the computing cores.

Other technical features may be readily apparent to one skilled in the art from the following figures, descriptions, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure and its features, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which:

FIGS. 1A through 1C illustrate an example general-purpose parallel computing architecture according to this disclosure;

FIGS. 2 and 3 illustrate example communications in the computing architecture of FIGS. 1A through 1C according to this disclosure;

FIGS. 4 and 5 illustrate example coprocessor functionality in the computing architecture of FIGS. 1A through 1C according to this disclosure;

FIG. 6 illustrates an example programmable coprocessor and reduction functionality in the computing architecture of FIGS. 1A through 1C according to this disclosure;

FIGS. 7 and 8 illustrate example computing systems using a general-purpose parallel computing architecture according to this disclosure;

FIG. 9 illustrates an example method for supporting advanced computing functions using a general-purpose parallel computing architecture according to this disclosure;

FIGS. 10 through 12 illustrate other example connectivity of components in a general-purpose parallel computing architecture according to this disclosure; and

FIGS. 13 through 19 illustrate example communication schemes in a general-purpose parallel computing architecture according to this disclosure.

DETAILED DESCRIPTION

FIGS. 1A through 19, discussed below, and the various embodiments used to describe the principles of the present invention in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the invention. Those skilled in the art will understand that the principles of the invention may be implemented in any type of suitably arranged device or system.

As noted above, the human brain is a massively parallel system that typically contains around 100 billion neurons connected by one quadrillion synapses. The synapses support the transport of signals between the neurons. The human brain is structured very differently from classical Turing machines. Simulating the human brain using a classical Turing machine is impractical given the large number of neurons and synapses typically in the human brain.

Although there are many components to human intelligence, one key component is dimensional reduction, which refers to the process of receiving a huge amount (high bandwidth) of sensory inputs and reducing the information down to a smaller amount (low bandwidth) of descriptive concepts. Mathematically, this reduction could be achieved using various forms of iterated factor analysis. The various forms of factor analysis tend to have several features in common. For example, in one mode of operation referred to as “forward explanatory mode,” the factor analyses perform some simple computation on a large number of inputs, accumulate a sum, and perform a possibly more complex computation on the output. In another mode of operation referred to as “backward learning mode,” the factor analyses alter the simple computation on the inputs by some simple computation on the output and corresponding input. Although these computations tend to be simple, the fan-in (referring to the number of inputs) and the fan-out (referring to the number of destinations an output is provided to) can both number in the tens of thousands.

Designing systems that can even somewhat rival the abilities of the human brain have generally been inadequate for a number of reasons. For example, such enormous fan-in and fan-out cannot be practically mapped into a two-dimensional (2D) circuit, which has kept such highly-connected computing architectures out of the mainstream. In order to design computing devices that rival the abilities of the human brain, a hardware architecture with more communication bandwidth is needed. This disclosure describes various new general-purpose “connectionist” hardware architectures that include a number of high-interconnected processing cores. Among other things, these hardware architectures can accelerate a broad class of algorithms in machine learning, scientific computing, video games, and other areas. In some embodiments, these hardware architectures can be manufactured at reasonable cost using modern techniques such as three-dimensional (3D) integrated circuit techniques.

FIGS. 1A through 1C illustrate an example general-purpose parallel computing architecture according to this disclosure. In particular, FIGS. 1A through 1C illustrate an example multi-level structure that provides a hardware architecture with high communication bandwidth. Different levels of the structure perform different functions as described below.

FIG. 1A illustrates a first level 100 of the hardware architecture. This level 100 includes multiple computing or processing cores 102, which are referred to as soma cores. In its minimal form, each soma core 102 can receive one or more data signals, perform some type of processing, and transmit one or more input signals. The structure included in each soma core 102 for performing processing operations can range from a very simple processing core to a very complex processing core. For example, the processing unit in each soma core 102 could be a relatively simplistic computing core, such as general-purpose single instruction, multiple data (SIMD) arithmetic unit. The soma cores 102 could also represent full processing cores, such as those from ARM, INTEL, or other computer processor manufacturers. In some embodiments, the group of soma cores 102 could be implemented using existing “many core” processor designs. However, any suitable computing cores could be used to implement the soma cores 102. While the hardware architecture here includes sixteen soma cores 102, any number of soma cores 102 could be supported in the hardware architecture. In particular embodiments, all of the soma cores 102 here could be implemented within a single integrated circuit chip that is referred to as a processor. Also, it should be noted that the soma cores 102 may or may not be homogenous.

Each soma core 102 includes processing circuitry 104 and at least one memory device 106. The processing circuitry 104 generally denotes circuitry used to perform some type of processing within the soma core 102. As noted above, the processing could be simplistic or complex, and the processing circuitry 104 can vary depending on the specific processing to be performed. The memory device 106 generally denotes any suitable storage and retrieval device(s), such as one or more registers, for storing data used, generated, or received by the soma core 102. In FIG. 1A, while the memory device 106 is shown as being embedded within a soma core 102, each memory device 106 could in whole or in part be located in any other suitable position(s) accessible to a soma core 102.

FIG. 1B illustrates a second level 110 of the hardware architecture, which is associated with the first level 100 of the hardware architecture. The second level 110 includes a number of coprocessors 112 (referred to as synapse coprocessors) associated with each soma core 102. The synapse coprocessors 112 generally process input data transmitted over signal lines (discussed below) between the soma cores 102. Each soma core 102 could be associated with multiple synapse coprocessors 112. As an example, for each soma core 102 in a group of N soma cores, up to N synapse coprocessors 112 could be provided and used to support communications from the soma cores 102 in the group (including itself) to that soma core 102. In some embodiments, each soma core 102 is communicatively coupled to one synapse coprocessor 112 for each of the soma cores 102 in the group. In other words, each soma core 102 can be communicatively coupled to all N soma cores 102 (via their respective synapse coprocessors 112), although other approaches (including those discussed below) need not do this. The synapse coprocessors 112 of a “local” or “host” soma core 102 are used to receive and process incoming input data from all soma cores 102 (including itself). This effectively allows all N synapse coprocessors 112 for each soma core 102 to receive input data from all N soma cores 102 in parallel in some embodiments. Note that each soma core 102 may typically include the same number of synapse coprocessors 112, although other embodiments could be used.

Each synapse coprocessor 112 includes any suitable structure supporting the processing of incoming input data for a soma core 102. The synapse coprocessors 112 could have limited capabilities and could be reprogrammable. In some embodiments, each synapse coprocessor 112 includes a programmable or other arithmetic unit 113 and at least one memory device 114. The arithmetic unit 113 denotes any suitable structure configured to execute one or more sequences of instructions to support various functions in the hardware architecture. Examples of these functions include receiving and processing of data in a specific sequence, performing an arithmetic operation on a received input and stored parameters, or forwarding values. The memory device 114 generally denotes any suitable storage and retrieval device(s), such as one or more registers, for storing data used, generated, or received by the synapse coprocessor 112. In FIG. 1B, while the memory device 114 is shown as being embedded within a synapse coprocessor 112, each memory device 114 could in whole or in part be located in any other suitable position(s) accessible to a synapse coprocessor 112.

The second level 110 of the hardware architecture also includes various reducer circuits or “reducers” 115. In some embodiments, there could be one reducer 115 for each soma core 102. Each reducer 115 receives output data that is produced by all of the synapse coprocessors 112 associated with one of the soma cores 102, processes the received output data in some way, and passes the result or results of the processing to the local soma core 102. For example, each reducer 115 could sum or otherwise accumulate received output data values, identify a minimum or maximum received output data value, or perform some other processing operation. In this way, each reducer 115 processes the output data for a soma core 102 and reduces the amount of data provided to that soma core 102.

Each reducer 115 includes any suitable structure for processing multiple output values. In some embodiments, each reducer 115 includes processing circuitry 116 and at least one memory device 117. The processing circuitry 116 generally denotes circuitry used to perform some type of processing within the reducer 115 and is often times much more specialized than the processing circuitry 104 of the soma cores 102. For instance, the processing circuitry 116 could include an adder tree formed by accumulators used to sum all of the output values from the synapse coprocessors 112 associated with one soma core 102. The memory device 117 generally denotes any suitable storage and retrieval device(s), such as one or more registers, for storing data used, generated, or received by the reducer 115. In FIG. 1B, while the memory device 117 is shown as being embedded within a reducer 115, each memory device 117 could in whole or in part be located in any other suitable position(s) accessible to a reducer 115.

FIG. 1C illustrates a third level 120 of the hardware architecture, which is associated with the first and second levels 100 and 110 of the hardware architecture here. The third level 120 includes multiple signal lines 122 and 124 that communicatively couple the soma cores 102, thereby supporting the transport of signals to, from, and between the soma cores 102. In some embodiments, the soma cores 102 are fully connected in that each soma core 102 in a group can communicate directly with all other soma cores 102 in the same group via the signal lines 122 and 124 and appropriate configuration of the synapse coprocessors 112. However, less than full connectivity could also be supported within the hardware architecture.

Note that the physical layout of the signal lines 122 and 124 in FIG. 1C is for illustration only and need not represent the actual physical arrangement of signal lines in the hardware architecture. For example, there are various ways to design a network between the soma cores 102, which may or may not support direct communication between all of the soma cores 102 and the synapse coprocessors 112 that receive input data from the soma cores 102. The signal lines 122 and 124 could therefore be arranged to support any desired communication paths in the hardware architecture. Also note that direct connections between each soma core 102 and its associated synapse coprocessors 112 are provided as an example at the logic level and not necessarily as a concrete implementation of a required network. Various mechanisms (including those described below) could be used to provide connections between each soma core 102 and its associated synapse coprocessors 112.

During operation, each soma core 102 operates to execute desired instructions and process data, possibly including data received from its reducer 115 or other source(s). Each soma core 102 can provide the results of its processing operations to other soma cores 102 (and possibly itself) as input data, and each soma core 102 could receive the input data generated by other soma cores' processing operations via its synapse coprocessors 112. The synapse coprocessors 112 for each soma core 102 can perform desired processing operations on the input data, and data output by the synapse coprocessors 112 can be further processed by the reducer 115 for each soma core 102. Results from the reducers 115 are provided to the local/host soma cores 102, which can use the data to perform additional processing operations.

It is also possible to support multiple “channels” in each communication from a soma core 102 to the connected synapse processors 112, where each channel can be associated with different processing operations. For example, each synapse coprocessor 112 could receive input data over multiple channels from one soma core 102, and the synapse coprocessors 112 connected to that soma core 112 could perform different processing operations depending on the channels used for the input data. Moreover, each reducer 115 could receive output data from its associated synapse coprocessors 112 for multiple channels, and the reducer 115 could perform different processing operations depending on the channel the output data was received from by the synapse processor 112. The channels could denote actual physical channels (such as when data is sent over different signal lines) or logical channels (such as when data is sent over a common signal line with different channel identifiers). In these embodiments, different registers or other memory locations in the soma cores 102, synapse coprocessors 112, and reducers 115 could be used to store different data and different programming instructions for different channels. This allows the hardware architecture to support concurrency or other types of programming operations.

As noted above, the memory device 114 of each synapse coprocessor 112 can include a number of registers. In some embodiments, the registers can include registers associated with each possible connection partner (each soma core 102) and used to hold incoming input data for each connection partner's channel(s). The registers could also include local registers used to hold parameter values and other values used during execution of programming instructions. In particular embodiments, processing operations of the synapse coprocessors 112 are described using one or more instructions executed in response to incoming input data, and there are no command loops in the synapse coprocessors 112.

Each soma core 102 could individually control the installation of program instructions on its synapse coprocessors 112, and different program instructions can be provided for different channels. For example, there might be an instruction causing a soma core 102 to load the same program to some or all of its synapse coprocessors 112. There might also be instructions causing the soma core 102 to load parameter registers of its synapse coprocessors 112, often with different values. Note that a soma core 102 could load all of this data from a given memory area that is large enough to hold values for all registers of all of the soma core's synapse coprocessors 112. Each soma core 102 could be allowed to read the individual parameter registers of its synapse coprocessors 112 but not the values of the per-channel registers. Instead, the values in the per-channel registers can be processed by the synapse processors 112 and/or be fed into the associated reducer 115, which can be programmed by the local/host soma core 102 to operate on the data received for each channel appropriately. The inputs to each reducer 115 can represent the output values from all synapse coprocessors 112 for the associated soma core 102 on a specific channel.

Each soma core 102 could support a number of instructions to facilitate the use of the synapse coprocessors 112 and the reducers 115 as described above. For example, each soma core 102 could support instructions for sending an input data element to (a specific channel of) all soma cores 102, for sending input data to a specific channel of its own synapse coprocessors 112, for receiving results from its own reducer 115, for installing or selecting programs or other instructions in its synapse coprocessors 112 and reducer 115, and for storing data in the parameter registers of the synapse coprocessors 112. Additional details of example instructions supported in the hardware architecture are provided below.

In some embodiments, the hardware architecture shown in FIGS. 1A through 1C could be implemented within a single integrated circuit chip. The integrated circuit chip could be fabricated in any suitable manner, such as by using long-standing fabrication techniques such as Silicon-on-Insulator (501) or more recently developed techniques such as three-dimensional integrated circuit fabrication techniques. If needed or desired, multiple instances of the hardware architecture shown in FIGS. 1A through 1C could be coupled together and used in order to expand the number of soma cores 102 available for use. For example, multiple integrated circuit chips could be communicatively coupled together to provide any desired number of soma cores 102, such as by coupling the signal lines 122 and 124 of each instance of the hardware architecture using one or more high-speed connections.

Also, in some embodiments, each soma core 102 could be configured to perform a specific function or a combination of functions in order to provide desired functionality in the hardware architecture. In other embodiments, each soma core 102 could be programmable so that the function(s) of the soma cores 102 can be defined and can change over time or as desired. Similarly, in some embodiments, each synapse coprocessor 112 and reducer 115 could be configured to perform a specific function or a combination of functions in order to provide desired functionality in the hardware architecture. In other embodiments, each synapse coprocessor 112 and reducer 115 could be programmable so that the function(s) of the synapse coprocessors 112 and reducer 115 can be defined and can change over time or as desired.

Note that the processing performed by the soma cores 102 can occur in parallel and that the processing performed by the synapse coprocessors 112 and the reducers 115 for each soma core 102 can also occur in parallel. In this way, each soma core 102 is able to communicate via multiple signal lines 122 and 124 at the same time given sufficient communication infrastructure between the soma cores 102. Given an adequate number of soma cores 102, synapse coprocessors 112, reducers 115, and signal lines 122 and 124, this hardware architecture can support a massive number of communication connections between computing cores, and those communication connections can all be available for use at the same time. As a result, this design represents a hardware architecture with more communication bandwidth.

Although FIGS. 1A through 1C illustrate one example of a general-purpose parallel computing architecture, various changes may be made to the hardware architecture shown in FIGS. 1A through 1C. For example, a hardware architecture could support any suitable number of soma cores, along with a suitable number of synapse coprocessors and reducers. Also, each soma core, synapse coprocessor, and reducer could be implemented in any other suitable manner, such as by using shared computing resources for the soma cores or synapse coprocessors or by using multiple reducers that allow performing more than one operation concurrently. In addition, various components in FIGS. 1A through 1C could be combined, further subdivided, rearranged, or omitted and additional components could be added according to particular needs. As a particular example, one or more soma cores 102 may not need to be used in conjunction with a reducer 115. As another particular example, FIGS. 10 through 12 (described below) show other possible layouts and connections between components of a general-purpose parallel computing architecture.

FIGS. 2 and 3 illustrate example communications in the computing architecture of FIGS. 1A through 1C according to this disclosure. As shown in FIG. 2, each soma core 102 can have synapse coprocessors 112 that receive input data from all soma cores 102 (including itself). This same pattern can be repeated for all soma cores 102 in a group of soma cores 102. The signal lines 122 and 124 described above can be used to couple each soma core 102 to one synapse coprocessor 112 of all soma cores 102 in a suitable manner to support these communications.

When there are N soma cores 102, each soma core 102 could be provided with N synapse coprocessors 112 (one synapse coprocessor 112 per soma core 102 including itself). Each soma core 102 can broadcast information to all soma cores 102, and each soma core 102 can receive information from all other soma cores 102 via its synapse coprocessors 112. Effectively, in some embodiments, the N synapse coprocessors 112 for each of the N soma cores 102 can support N independent communication networks between the soma cores 102.

FIG. 3 illustrates one specific example of two of the independent communication networks between soma cores. As shown in FIG. 3, one soma core 102 a can broadcast input data to one synapse coprocessor 112 of each soma core 102 in the system. Similarly, another soma core 102 b can broadcast data to one synapse coprocessors 112 of each soma core 102 in the system. The broadcasting by the soma cores 102 a and 102 b can, in some embodiments, occur simultaneously. As a result, N soma cores 102 can engage in N broadcasts of data simultaneously.

Note that while the broadcasting here is shown as occurring serially from one soma core to the next in rows and columns, this is for ease of illustration only. Each synapse coprocessor 112 that is broadcasting data could alternatively broadcast the data directly to synapse coprocessors 112 of all soma cores 102 via the signal lines 122 and 124. Of course, if needed or desired, it is also possible to allow multiple soma cores 102 to broadcast over the same signal lines 122 and 124, such as with some sort of addressing or contention mechanism in place.

Although FIGS. 2 and 3 illustrate examples of communications in the computing architecture of FIGS. 1A through 1C, various changes may be made to FIGS. 2 and 3. For example, a hardware architecture could support any suitable number of soma cores, along with a suitable number of synapse coprocessors. Also, various components in FIGS. 2 and 3 could be combined, further subdivided, rearranged, or omitted and additional components could be added according to particular needs. In addition, any suitable communications amongst the soma cores 102 could be supported.

FIGS. 4 and 5 illustrate example coprocessor functionality in the computing architecture of FIGS. 1A through 1C according to this disclosure. In particular, FIGS. 4 and 5 illustrate example mechanisms for implementing the synapse coprocessors 112 described above. Note that these example implementations are for illustration only and that the synapse coprocessors 112 could be implemented in other ways.

As shown in FIG. 4, a synapse coprocessor 112 for the j^(th) soma core 102 can be implemented using the arithmetic unit 113 described above. The arithmetic unit 113 performs one or more desired computations using incoming input data received from the i^(th) soma core 102. The arithmetic unit 113 then outputs the resulting output data to a reducer 115 associated with the j^(th) soma core 102. The reducer 115 can process the outputs from multiple arithmetic units 113 of multiple synapse coprocessors 112 associated with the j^(th) soma core 102 and provide the result(s) to the j^(th) soma core 102.

The operation(s) performed by the arithmetic unit 113 in FIG. 4 could be defined or controlled using a program (φ) 402, and the program 402 operates using one or more parameters 404. The program 402 and the parameter(s) 404 can be stored within the memory device 114 or other location(s). The one or more parameters 404 can be set or controlled by the synapse coprocessor 112, by the associated soma core 102, or in any other suitable manner. Example operations that could be performed by the arithmetic unit 113 can include adding, subtracting, or multiplying values; generating a constant value across all synapse coprocessors 112 associated with a soma core 102; outputting an identifier for the synapse coprocessor 112; selecting one of multiple values based on a test value; or calculating the sign or inverse square root of a value.

As shown in FIG. 5, there can be multiple operations or sets of operations performed within the hardware architecture. A “channel identifier” value can be used by the synapse coprocessor 112 to identify which of multiple selectable programs (φ) 502 are to be executed by the arithmetic unit 113 on incoming data. The “channel identifier” can also be used to control which parameter(s) 504 are used by the arithmetic unit 113 and where results generated by the arithmetic unit 113 are sent. The selectable programs 502 and the parameters 504 could be stored in the memory device 114 of the synapse coprocessor 112 or in other location(s).

In some embodiments, each of the arithmetic units 113 and the reducers 115 could be implemented in a pipelined fashion, and incoming data could denote scalar values or small vectors of values. In these embodiments, multiple scalar values or at least one vector of values could be received from the soma core 102, and a single program 502 or different programs 502 could be applied to the values by the arithmetic unit 113 to produce a sequence of output values. The sequence of output values could be provided to the reducer 115 for further processing.

Although FIGS. 4 and 5 illustrate examples of coprocessor functionality in the computing architecture of FIGS. 1A through 1C, various changes may be made to FIGS. 4 and 5. For example, each synapse coprocessor 112 could be implemented in any other defined or reconfigurable manner.

FIG. 6 illustrates an example programmable coprocessor and reduction functionality in the computing architecture of FIGS. 1A through 1C according to this disclosure. In particular, FIG. 6 illustrates an example mechanism for controlling the programming of the synapse coprocessors 112 and the reducers 115 described above.

As shown in FIG. 6, a reducer 115 is configured to receive the output data from multiple synapse coprocessors 112 associated with a soma core 102. The reducer 115 then performs at least one operation (identified by Ψ) using the outputs from the synapse coprocessors 112 to generate at least one result that is provided to the associated soma core 102. The one or more computations performed by the reducer 115 could include any suitable operations performed using the outputs from multiple synapse coprocessors 112. In some embodiments, the reducer 115 could execute one or more sequences of instructions to support various functions in the hardware architecture. For example, after receiving data from the coprocessors 112 of the associated soma core 102 in parallel, the reducer 115 could perform a programmable operation on the received data and output the result(s) to the associated soma core 102. Example operations can include summing or multiplying the outputs from all synapse coprocessors 112, identifying a minimum or maximum output from the synapse coprocessors 112, or selecting a specific synapse coprocessor's value as the output.

A memory device 602 can be used in this structure to store one or more programs (φ) executed by the synapse coprocessors 112. The memory device 602 can also be used to store one or more programs (Ψ) executed by the reducer 115. The memory device 602 represents any suitable volatile or non-volatile storage and retrieval device or devices, such as part of one or more of the memories 106, 114, 117.

Although FIG. 6 illustrates one example of programmable coprocessor and reduction functionality in the computing architecture of FIGS. 1A through 1C, various changes may be made to FIG. 6. For example, a hardware architecture could support any suitable number of soma cores, along with a suitable number of synapse coprocessors and reducers. Also, various components in FIG. 6 could be combined, further subdivided, rearranged, or omitted and additional components could be added according to particular needs.

FIGS. 7 and 8 illustrate example computing systems using a general-purpose parallel computing architecture according to this disclosure. As shown in FIG. 7, a computing system 700 includes at least one processor 702, at least one storage device 704, at least one communications unit 706, and at least one input/output (I/O) unit 708.

The processor 702 could denote an integrated circuit chip incorporating the soma cores 102, synapse coprocessors 112, reducers 115, and signal lines 122 and 124 described above. The processor 702 executes instructions, such as those that may be loaded into a memory device 710 and then loaded into the registers or other memories of the soma cores 102, synapse coprocessors 112, and reducers 115. The processor 702 may include any suitable numbers of soma cores 102, synapse coprocessors 112, reducers 115, and signal lines 122 and 124.

The memory device 710 and a persistent storage 712 are examples of storage devices 704, which represent any structure(s) capable of storing and facilitating retrieval of information (such as data, program code, and/or other suitable information on a temporary or permanent basis). The memory device 710 may represent a random access memory or any other suitable volatile or non-volatile storage device(s). The persistent storage 712 may contain one or more components or devices supporting longer-term storage of data, such as a read only memory, hard drive, Flash memory, or optical disc.

The communications unit 706 supports communications with other systems or devices. For example, the communications unit 706 could include a network interface card or a wireless transceiver facilitating communications over a wired or wireless network. The communications unit 706 may support communications through any suitable physical or wireless communication link(s).

The I/O unit 708 allows for input and output of data. For example, the I/O unit 708 may provide a connection for user input through a keyboard, mouse, keypad, touchscreen, or other suitable input device. The I/O unit 708 may also send output to a display, printer, or other suitable output device.

If needed or desired, multiple instances of the hardware architecture shown in FIGS. 1A through 1C could be coupled together and used in order to expand the number of soma cores 102 available for use. For example, multiple integrated circuit chips could be communicatively coupled together to provide any desired number of soma cores 102. An example of this is shown in FIG. 8, where a multi-processor arrangement 800 could be used in the computing system 700 as the processor 702 or in another computing system. The multi-processor arrangement 800 here includes at least two processors coupled by at least one high-speed connection. In this example, four processors 802-808 are coupled by four high-speed connections 810 in a ring, although any other suitable numbers and arrangements of processors and high-speed connections could be used.

Each high-speed connection 810 can support any suitable communication path(s) for coupling multiple instances of the hardware architecture shown in FIGS. 1A through 1C. For example, each high-speed connection 810 can be communicatively coupled to the third level 120 of each instance of the hardware architecture so that the high-speed connection 810 supports the transport of signals between the signal lines 122 and/or 124 of the hardware instances. Each high-speed connection 810 includes any suitable structure for transporting signals between hardware instances, such as between multiple integrated circuit chips.

Various types of high-speed connections 810 could be used to support a multi-processor architecture. For example, each high-speed connection 810 could be implemented using a photonic connection between two integrated circuit chips. As another example, the integrated circuit chips themselves could support “quilt” packaging, where each integrated circuit chip includes electrical connections along at least one side and the integrated circuit chips are mounted so that electrical connections on different chips contact one another. Note, however, that any other or additional high-speed connections 810 could also be used.

Although FIGS. 7 and 8 illustrate examples of computing systems using a general-purpose parallel computing architecture, various changes may be made to FIGS. 7 and 8. For example, the hardware architecture shown in FIGS. 1A through 1C could be used in any other suitable system to perform any suitable functions.

FIG. 9 illustrates an example method 900 for supporting advanced computing functions using a general-purpose parallel computing architecture according to this disclosure. For ease of explanation, the method 900 is described with respect to the hardware architecture shown in FIGS. 1A through 1C. However, the method 900 could be used with any other suitable hardware architecture.

As shown in FIG. 9, processing operations are executed using multiple parallel computing cores at step 902. This could include, for example, the soma cores 102 in one or more processors executing instructions to perform any of a wide variety of computations. The processing operations could denote simplistic operations performed by SIMD soma cores 102 up to complex operations performed by full-processor soma cores 102. Note that the operations shown in FIG. 9 can be executed in order because of dependencies of the operations. Multiple independent chains of the same operations can be performed concurrently and communication and synapse/reducer operations can be performed in parallel using channel addressing as described above.

The processing results from each computing core are published to other computing cores at step 904. This could include, for example, each soma core 102 providing its processing results over the signal lines 122 and 124 to one synapse coprocessor 112 of each soma core 102. In some embodiments, this results in the synapse coprocessors 112 for each soma core 102 receiving the processing results from all of the soma cores 102.

For each computing core, the processing results from the computing cores are processed at step 906 and reduced at step 908. This could include, for example, the synapse coprocessors 112 associated with each soma core 102 performing some type of processing on the processing results from all of the soma cores 102. Specific examples of the types of operations that could be performed by the arithmetic unit 113 of the synapse coprocessors 112 are described below. This could also include the reducer 115 for each soma core 102 processing the outputs of the synapse coprocessors 112 for that soma core 102. Specific examples of the types of operations that could be performed by the reducer 115 are described below. Note that the operations performed by the synapse coprocessors 112 and the reducers 115 could be controlled and can vary, such as when different programs φ and Ψ are used for different channels of data.

The reduced results are provided to the computing cores at step 910. This could include, for example, the reducers 115 providing outputs to their associated soma cores 102. At this point, the method 900 could be repeated, with the computing cores using the reduced results during further execution of the processing operations. Alternatively, the method 900 could end and be repeated later with new data.

Although FIG. 9 illustrates one example of a method 900 for supporting advanced computing functions using a general-purpose parallel computing architecture, various changes may be made to FIG. 9. For example, while shown as a series of steps, various steps in FIG. 9 could overlap, occur in parallel, occur in a different order, or occur any number of times.

In the description of the architecture shown in FIGS. 1A through 1C above, the architecture is described as being a multi-level structure. For example, the synapse coprocessors 112 and reducers 115 could be located above the soma cores 102, and the signal lines 122 and 124 could be located above the synapse coprocessors 112 and reducers 115. However, there are a large number of physical layouts that could be used for the components when forming the overall architecture. The exact layout used for a particular architecture could be selected or designed based on a number of factors and could vary as needed or desired. Also, certain approaches could be used to help optimize a layout, such as by minimizing communication path lengths, minimizing the space occupied by the components of the architecture, or minimizing manufacturing or assembly costs. While the following describes example physical layouts that could be used, these layouts are for illustration only, and a number of additional layouts may be known or developed by those skilled in the art.

FIGS. 10 through 12 illustrate other example connectivity of components in a general-purpose parallel computing architecture according to this disclosure. For ease of explanation, the connections are described with respect to the components of the architecture shown in FIGS. 1A through 1C.

As shown in FIG. 10, a layout 1000 includes the soma cores 102, a subset of which are shown here. Also, in FIG. 10, the synapse coprocessors 112 for each soma core 102 are shown as being vertically aligned above that soma core 102. In between each soma core 102 and its synapse coprocessors 112 is a reducer 115. Each soma core 102 sends data to its respective synapse coprocessor 112 for each soma core 102 (meaning to one synapse coprocessor 112 in each column) using its respective signal line 1002. The results of the computations in the synapse coprocessors 112 are sent to the reducers 115 for the soma cores 102 via signal lines 1004. Each reducer 115 sends a result back to its soma core 102 via a respective signal line 1006.

In some embodiments, communication on the signal lines 1002 and/or 1004 can be point-to-point, where a synapse coprocessor 112 receives data and then forwards it to the next synapse coprocessor 112 on the line. In other embodiments, each signal line 1002 and/or 1004 includes multiple separate signal lines (such as up to N signal lines). In these embodiments, each signal line 1002 could connect a soma core 102 directly to each synapse coprocessor 112 on the signal line 1002, and each signal line 1004 could connect all synapse coprocessors 112 directly with the associated reducer 115.

In still other embodiments, each reducer 115 can be integrated into its associated soma core 102, and no signal lines 1006 are needed. The reducers 115 in this case can be implemented using the computing functionality of the soma cores 102, or the reducers 115 could have their own compute functionality.

As shown in FIG. 11, a layout 1100 includes the soma cores 102, a subset of which are shown here. The soma cores 102 in FIG. 11 are shown as in FIG. 10, and they send data through signal lines 1102. However, in FIG. 11, each soma core 102 is associated with multiple coprocessor/reducer cores 1104, rather than coprocessors 112 and a separate reducer 115. The coprocessor/reducer cores 1104 are functional units that combine the functionality of the coprocessors 112 and parts of the functionality of the reducers 115. The reducers' functionality can be distributed when certain types of operations are used in the reducers 115, such as associative operations like summing values or finding a minimum or maximum value. The use of associative operations allows intermediate results to be generated in some of the coprocessor/reducer cores 1104. The last coprocessor/reducer core 1104 in the chain for each soma core 102 generates the final reducer result. This can reduce the total length of signal lines 1106, possibly simplifying the physical layout.

Each coprocessor/reducer core 1104 includes any suitable structure supporting the processing of incoming input data for a soma core 102. At least some of the coprocessor/reducer cores 1104 also include any suitable structures supporting binary associative or other reduction operations.

The signal lines 1106 couple the coprocessor/reducer cores 1104 to one another and to the soma cores 102. Several signal lines 1106 here are shown as loops, going from one coprocessor/reducer core 1104 to the same coprocessor/reducer core 1104. These signal lines 1106 could denote internal communications within those coprocessor/reducer cores 1104 and need not represent actual pathways outside of the coprocessor/reducer cores 1104.

In some embodiments, only those coprocessor/reducer cores 1104 that receive data from the signal lines 1106 may include reduction functionality, while the remaining coprocessor/reducer cores 1104 could denote synapse coprocessors only. In FIG. 11, for instance, the coprocessor/reducer cores 1104 in the first, third, fifth, and seventh rows could denote synapse coprocessors only, while the coprocessor/reducer cores 1104 in the second, fourth, sixth, and eighth rows could denote synapse coprocessors with reduction functionality.

Thus, in the example shown in FIG. 11, each of the coprocessor/reducer cores 1104 in the second row can sum two values or find a minimum or maximum of two values (its own value and a value from the first row) and output the result. Each of the coprocessor/reducer cores 1104 in the fourth row can sum three values or find a minimum or maximum of three values (its own value, a value from the second row, and a value from the third row) and output the result. Each of the coprocessor/reducer cores 1104 in the sixth row can sum two values or find a minimum or maximum of two values (its own value and a value from the fifth row) and output the result. Each of the coprocessor/reducer cores 1104 in the eighth row can sum four values or find a minimum or maximum of four values (its own value, a value from the fourth row, a value from the sixth row, and a value from the seventh row) and output the result. The result from each coprocessor/reducer core 1104 in the eighth row would denote the sum or maximum/minimum value for the associated column.

Note that this represents one way in which the functionality of the reducers 115 could be distributed, and it is specific to an embodiment in which eight soma cores 102 are used. Other approaches could also be used, such as other approaches using a different number of soma cores 102 and a different number of associated coprocessors. Also note that summing values and finding minimum/maximum values are merely examples of the types of operations that could be distributed in the coprocessor/reducer cores 1104.

Further note that the number of inputs and the source(s) of the input values used by the reduction functionality can vary as needed or desired, and the exact positions of the coprocessor/reducer cores 1104 implementing the reduction functionality can vary as needed or desired. For example, the number of inputs can vary depending on the overall size of the architecture, such as the number of soma cores and the associated number of coprocessors. Also, the inputs that are used for the reduction operations need not only come from the coprocessor/reducer cores 1104. The inputs used for the reduction operations could also or alternatively come from one or more external agents, such as when the inputs include outputs from other reducers. This is in contrast to the example shown in FIG. 10, where a monolithic reducer implementation is used and all synapse coprocessors 112 in a column communicate with one reducer 115. Other possible implementations might have one reducer per column and one or more additional reducers per chip/semiconductor die, where the additional reducer(s) can be used to reduce communication traffic between multiple chips/semiconductor dies.

The signal lines 1102 and 1106 can be used to couple the components together in a suitable manner, and the signal lines 1102 and 1106 can be fabricated using any suitable technique(s). Depending on the implementation, the components in FIG. 11 could be formed in a single device or in multiple devices that are coupled together. For example, all of the components shown in FIG. 11 could be fabricated in a single integrated circuit chip, or different components shown in FIG. 11 could be fabricated in different integrated circuit chips that are coupled together using electrical connections like serial point-to-point connections, a high-speed bus, or other connections.

FIG. 12 illustrates an example layout 1200 in which multiple integrated circuit chips 1202 and 1204 are used to implement the soma cores 102, the synapse coprocessors 112, and the reducers 115. Note that the coprocessor/reducer cores 1104 could be used instead of separate synapse coprocessors 112 and reducers 115 here. Also note that, as described above, at least one additional reducer 115 could be used to further reduce the data sent between the integrated circuit chips 1202 and 1204.

One or more communication links 1206 or other communication interfaces could be used to couple the components in different integrated circuit chips 1202 and 1204. For example, the communication link(s) 1206 could include connections from the soma cores 102 in the chip 1202 to the synapse coprocessors 112 in the chip 1204, as well as connections from the reducers 115 in the chip 1204 to the soma cores 102 in the chip 1202. This type of layout may allow different combinations of integrated circuit chips containing different numbers or types of soma cores 102 and synapse coprocessors 112/reducers 115.

Although FIGS. 10 through 12 illustrate examples of physical layouts of components in a general-purpose parallel computing architecture, various changes may be made to FIGS. 10 through 12. For example, a hardware architecture could support any suitable number of soma cores, along with a suitable number of synapse coprocessors, reducers, coprocessor/reducer cores, or signal lines. Also, as noted above, a wide variety of physical layouts could be used, and FIGS. 10 through 12 do not limit this disclosure to only the illustrated layouts.

FIGS. 13 through 19 illustrate example communication schemes in a general-purpose parallel computing architecture according to this disclosure. The actual implementation of a network or other communication mechanism to support data transport between the soma cores 102 and their synapse coprocessors 112 can take on many different forms. The following describes several specific examples of these communication mechanisms, but any other suitable communication scheme can be used to transport data between the soma cores 102 and their synapse coprocessors 112. Also, the example communication schemes provided below apply equally to implementations that do or do not have the soma cores 102 and their respective synapse coprocessors 112 physically collocated.

Assume an implementation with N soma cores 102 and N synapse coprocessors 112 per soma core 102. In FIG. 13, each soma core 102 has a single connection 1302 to one of its synapse coprocessors 112, and the remaining synapse coprocessors 112 that soma core 102 are daisy-chained together. The first synapse coprocessor 112 in the chain receives data from the soma core 102, and all other synapse coprocessors 112 in the chain receive data from the previous synapse coprocessor 112 in the chain. In this example, the synapse coprocessors 112 receive data from the soma core 102 in sequence, one after the other, until all synapse coprocessors 112 of the soma core 102 have the data.

The use of a single daisy chain is not required. For example, in FIG. 14, each soma core 102 can have multiple connections 1402 to multiple chains of synapse coprocessors 112. The first synapse coprocessor 112 in each chain receives data from the soma core 102, and the data is passed in sequence through the synapse coprocessors 112 in each chain. The data can be provided to the different chains in parallel, allowing for faster delivery of the data to all synapse coprocessors 112 compared to FIG. 13. Note that while two chains are shown here, any number of synapse coprocessor chains could be used.

The use of daisy chaining is also not required. For instance, in FIG. 15, a soma core 102 can have a dedicated connection 1502 to each of its synapse coprocessors 112. Here, the synapse coprocessors 112 receive data directly from the soma core 102, and all of the synapse coprocessors 112 could receive the data in parallel.

It is also possible to support communication from a single soma core 102 to one of its synapse coprocessors 112 and branch the communications from that synapse coprocessor 112. For example, FIG. 16 illustrates that a single connection 1602 couples the soma core 102 to one synapse coprocessor 112, and multiple connections 1604 couple that synapse coprocessor 112 to multiple chains of synapse coprocessors 112. Data can be provided from the soma core 102 to the first synapse coprocessor 112, and the data can then be provided into the multiple chains of synapse coprocessors 112 in parallel. Note that while three chains of synapse coprocessors 112 are shown here, any number of chains could be used. Also note that more than one synapse coprocessor 112 can receive the data from the soma core 102 directly before branching the communication from these two or more synapse coprocessors 112.

It is further possible to arrange the synapse coprocessors 112 in a tree or other multi-level hierarchy. For example, FIG. 17 illustrates that a single connection 1702 couples the soma core 102 to one synapse coprocessor 112. Multiple connections 1704 couple that synapse coprocessor 112 to another level of synapse coprocessors 112, and multiple connections 1706 couple that level of synapse coprocessors 112 to yet another level of synapse coprocessors 112. This configuration can be repeated additional times to support the use of synapse coprocessors 112 on any suitable number of hierarchical levels. Note that while, moving left to right, each synapse coprocessor 112 is coupled to three synapse coprocessors 112 in the next level, this is for illustration only. Any other suitable tree configuration could be supported as needed or desired. Note that another possible arrangement has more than one tree, meaning more than one synapse coprocessor 112 receives data directly from the soma core 102 and serve as root nodes of individual trees.

While the layouts in FIGS. 13 through 17 illustrate example configurations of communication paths, these are for illustration only. Various combination of these approaches could also be used, as long as each synapse coprocessor 112 can receive data from its associated soma core 102. Also, other or additional approaches could also be used, such as a mesh network that communicatively couples the soma core 102 to neighboring synapse coprocessors 112, which then pass along data to other synapse coprocessors 112 through mesh networking. An appropriate structure of the mesh guarantees that each synapse coprocessor 112 receives the data.

While the designs for the communication schemes so far have assumed that a soma core can privately communicate with its synapse coprocessors 112, this need not be the case. For example, as shown in FIG. 18, one possible alternative implementation is to use a virtual network 1802 for the soma cores 102, where data is effectively routed from the soma cores 102 to their synapse coprocessors 112 via the network 1802. The virtual network 1802 could be implemented using logic executed by the synapse coprocessors 112 themselves or using components external to the synapse coprocessors 112.

To implement a virtual network 1802, each data package sent over the virtual network 1802 has meta information that allows the data package to reach the correct destination(s). There are various ways of specifying this meta information. For example, in some embodiments, each data package could have an identifier for the originating soma core 102. Using a routing table 1804 (either static or dynamic), data packages can be forwarded from their respective soma cores 102 to the appropriate synapse coprocessors 112. One specific implementation may involve the use of a static routing table for each synapse coprocessor 112, where the address is used as an index into the routing table. In other embodiments, each data package could have one or more destination addresses specified by the sending soma core 102, and the virtual network 1802 can route the data packages according to their target addresses. Any suitable mechanism can be used to specify the originating soma cores' identifiers or the target addresses. Example mechanisms include attaching explicit information to each data package or storing each data package at a specific address (such as in the soma cores' address spaces), where the specified address implicitly conveys the required information.

As yet another example, it is possible to implement communications using a resource that is shared by two or more participants (soma cores 102 or synapse coprocessors 112). At least one participant has write access to the shared resource, and at least one other participant has read access to the shared resource. The shared resource could be implemented in various ways. For example, a “store and forward” network denotes a network in which data is stored by one or more components and retrieved (forwarded) by one or more components. A “store and forward” network allows each soma core 102 to communicate data to the synapse coprocessors 112 by storing the data at specific addresses, and the synapse coprocessors 112 can then read the data from the same addresses.

An example is shown in FIG. 19, where a shared memory 1902 is used to transfer data from the soma cores 102 to the coprocessor/reducer cores 1104 (although the synapse coprocessors 112 and reducers 115 could also be used). The shared memory 1902 includes a number of memory locations 1904. The soma cores 102 can write data to those memory locations 1904, and the synapse coprocessors 112 or coprocessor/reducer cores 1104 can read the data from those memory locations 1904. This can be done in a manner that is optimized internally for the communication pattern of soma cores 102 broadcasting to synapse coprocessors 112 or to coprocessor/reducer cores 1104.

In this example, memory interfaces 1906 and 1908 are provided and are used to write data to or receive data from the memory locations 1904. Each of the memory interfaces 1906 and 1908 can receive an address, and the memory interface 1906 can also receive data. The memory interface 1906 writes the received data to the received address, and the memory interface 1908 reads requested data from the received address. Note, however, that the memory interfaces 1906 and 1908 could be omitted if the soma cores 102 and the synapse coprocessors 112 or coprocessor/reducer cores 1104 are configured to read from and write to specified memory locations.

The synapse coprocessors 112 or coprocessor/reducer cores 1104 could access the shared memory 1902 in any suitable manner. For example, the synapse coprocessors 112 or coprocessor/reducer cores 1104 could poll the shared memory 1902 to identify new data, or the synapse coprocessors 112 or coprocessor/reducer cores 1104 could receive out-of-band notifications when data is stored in the shared memory 1902.

It is possible to have a software implementation supporting this design, such as one where the shared memory 1902 is implemented using variables to transfer data between components. Of course, such variables would be stored in memory of the executing device, but the memory would require no special configuration. The functionality shown in FIG. 19 could also be implemented in other ways. For example, special-purpose hardware that implements mailboxes or other segregated memory space could also be used to facilitate communications.

In some embodiments, there may be N soma cores 102, but each soma core 102 may not have N synapse coprocessors 112. Instead, each soma core 102 may implement N “logical” synapse coprocessors using a smaller number of actual synapse coprocessors 112. In those embodiments, a subset of the logical communication links can be implemented physically, and the different methods described above can be simplified.

Although FIGS. 13 through 19 illustrate examples of communication schemes in a general-purpose parallel computing architecture, various changes may be made to FIGS. 13 through 19. For example, any number of other or additional techniques could be used to transfer data between soma cores 102 and associated synapse coprocessors 112. Also, any of the techniques shown here could be used in architectures that include synapse coprocessors 112 and reducers 115 or coprocessor/reducer cores 1104.

In some of the embodiments described above, each soma core 102 can program its synapse coprocessors 112 to execute at least one program φ, and the program(s) φ can be executed as soon as incoming data arrives. The reducer 115 for a soma core 102 executes at least one program ‘I’ using the results of program φ from all of the synapse coprocessors 112 for that soma core 102. In particular embodiments, each program φ can often execute in O(1) time given a fixed vector size and no loops, and the program Ψ can often execute in O(log N) time. Also, in particular embodiments, the collective processing performed by the synapse coprocessors 112 and the reducer 115 for each soma core 102 could be expressed as: y _(j)=(Ψ_(j))_(i=1) ^(N)φ_(j)(x _(i) ,p _(ij))  (1) Here, i denotes the identity of a sender soma core 102 (or the identity of a soma core 102 plus a soma group identifier of the soma core 102), and N denotes the number of soma cores 102 (or the number of soma cores 102 times the number of soma groups). Also, j denotes a channel identifier, and p denotes one or more parameters (such as parameters 402 or 502) used in the synapse coprocessors 112 (such as state or local variables, which may or may not be channel-specific). Further, x_(i) denotes the output of the i^(th) soma core 102, and y_(j) denotes the output provided by a reducer 115 as a result to the soma core 102 in channel j. In addition, φ_(j)( ) denotes the function performed by the synapse coprocessors 112 for channel j^(th) using the incoming data x_(i) and possibly the parameters p, and Ψ( ) denotes the function performed by the reducer 115 for the local soma core 102 using the outputs of the synapse coprocessors 112.

Examples of the φ_(j)( ) functions could include:

-   -   r=x*a+b     -   r=x/√{square root over (a)}+b     -   r=max(x,c)     -   r=min(x,c)     -   r=select(x,a,b)     -   r=index         Here, a, b, c, and r could denote names of registers in a         synapse coprocessor 112, and x could denote an input value from         a soma core 102 (although another register of the synapse         coprocessor 112 could also be used instead). The select         operation tests the condition in the first parameter (such as by         performing a simple non-zero test) and returns either the second         parameter or the third parameter based on the result of the         test. The index operation may be specific to an implementation         with multiple soma groups. Each soma group could include the         same number of soma cores 102. More details of soma groups are         provided below. In sonic embodiments, none of the functions         implemented by the synapse coprocessors 112 involves loops.

Examples of the Ψ( ) functions could include:

-   -   v=sum(r[i])     -   v=max(r[i])     -   v=min(r[i])         Here, v denotes the output of a reducer 115 provided to a soma         core 102, and r[i] denotes the inputs received by the reducer         115 from the synapse coprocessors 112 (multiple values from the         same synapse coprocessor 112 could be obtained in an         implementation with multiple soma groups). Each of the max and         min functions could return both (i) the maximum or minimum value         and (ii) the index value i of the synapse coprocessor 112 that         provided the maximum or minimum value. The result of the Ψ( )         function could be made available to the soma core 102 using one         or more registers.

In these embodiments, the synapse coprocessors 112 might not be programmed with a traditional program that runs in a loop and that actively retrieves (and if necessary waits for) input. Instead, each channel can be associated with a program φ, and the program φ can be marked as executable when data arrives for the channel and eventually executed when compute resources become available. When all synapse coprocessor programs φ finish, the result of the reduction program Ψ can be computed. The computation of the result by the reduction program Ψ could start as soon as a minimal number of the synapse coprocessor results are available, with caveats such as the one mentioned below. The results of the reduction program Ψ can be saved in per-channel registers. When a soma core 102 issues an instruction to read a reduction result, the reducer 115 may then be ready to produce the next reduction result for that channel. Until then, operation of the reducer 115 for that channel could be blocked.

The allocation of registers in the synapse coprocessors 112 and reducers 115 and the allocation of channels can be abstracted if desired. For example, instead of referring to an absolute index for each of these resources in a program specification, an allocation mechanism could be used to achieve the equivalent of multi-program execution. For example, when a program (including the φ and Ψ programs) is loaded, the actual registers used can be chosen from available registers of a register file, and an available channel can be selected. No explicit concurrency has to be created since the program is invoked based on incoming data. Upon finishing the program, the used resources in terms of registers and channels can be made available again. The actual instructions executed by the synapse coprocessors 112 and reducers 115 do not have to know about any of this. Rather, the instructions of the uploaded program code could use absolute register numbers or indices, and the abstraction can occur at a higher level where the program loading by the soma core 102 is preceded by appropriate code generation or rewriting based on the needs of the program and the available resources.

One example caveat to the computation of a result by a reduction program Ψ starting as soon as a minimal number of synapse coprocessor results are available is as follows. Depending on the operation and possibly the data type, the hardware architecture could support a mode that can significantly speed up execution of the program Ψ at the expense of repeatability by not following a specified order of operations. For example, floating-point operations do not follow associativity rules because of the possibility of cancellation. A specific example of this is when floating-point additions must be performed in the same order to guarantee producing the exact same result each time. This could create slowdowns in cases where one input value is not yet available while other input values later in the order of operations are available. The reducer 115 could be programmed to either wait for the input values so that the operation order is always maintained (resulting in slowdowns), or the reducer 115 could be programmed to perform the sums out of order (allowing results to be obtained more quickly but with potentially less repeatability).

As noted above, an implementation of the hardware architecture can include more than one group of soma cores 102. Such an approach could implement the soma groups in a single integrated circuit, or different soma groups could be implemented as separate integrated circuits (and the integrated circuits can be coupled together, such as with electrical or optical connections). Several types of programs (including those discussed in more detail below) can be sped up significantly with this type of hardware architecture if an entire data set can be mapped to the soma cores 102.

To facilitate solutions with multiple soma groups, some resources and operations may be duplicated depending on the number of communication partners of each synapse coprocessor 112. For example, in a simple model, each synapse coprocessor 112 could receive results from exactly one soma core 102. In a solution with multiple soma groups, each synapse coprocessor 112 could receive results from one soma core 102 per soma group. In the synapse coprocessor programs, this can be expressed just like in an implementation with a single soma group if the resources related to data transfers (such as a register to hold transmitted data and a register to hold a result) are duplicated. A single processor can be therefore be implemented to work with up to S soma groups in case there are S duplicates for each synapse coprocessor register. To enable per-soma group parameters, it may be useful or necessary to provide access to the soma group number that is the source of the data. This could be achieved using the index operation described above, which returns the soma group number in addition to the soma core index used for a specific communication.

The implementation of multiple soma groups, if they are physically separated, could be achieved in any suitable manner, such as by coupling multiple integrated circuits using photonics or other high-speed interconnects. In cases where each soma core 102 writes its results to a dedicated bus, the respective buses of the different soma cores 102 in each soma group can be connected, which changes each bus from a 1:N communication bus to an S:N bus. This can be permitted, for instance, if transmitted data carries a full address, such as in the most general form [soma group ID, soma ID, channel ID], allowing the data to be routed on a per-soma group basis as long as it can be ensured that a synapse coprocessor 112 on each soma core 102 in each soma group receives the data.

In addition, there are a number of possible approaches for implementing the network(s) used to couple the soma cores 102 to the synapse coprocessors 112 using the signal lines 122 and 124. For example, as described above, each of N independent networks can have one of N soma cores 102 as a source and connects that soma core 102 to N synapse coprocessors 112 (one of each soma core 102). While a dedicated network for each output of each soma core 102 would minimize possible contention in data transfers, it means that resources go unused when no transmissions are occurring. Ideally, all of the soma cores 102 work in lockstep and transmit data at approximately the same time, which could be handled well only with dedicated signal lines. In reality, the soma cores 102 can lose sync due to various factors, such as minute effects in execution like waiting for resources or different dynamic decisions like branch predictions. In that case, the transmissions would not happen at exactly the same time. Since the transmitted data is usually small, the use of one (or a small number) of networks to connect the soma cores 102 might suffice without significant slowdowns, and it would provide improved utilization of resources. Note that in the address [soma group ID, soma ID, channel ID] described above, the soma ID can be dropped if each soma core 102 per soma group has its own dedicated network connecting it to a synapse coprocessor 112 on each soma core 102. Another implementation of the connection network could have one single network per soma group, and all data packages have complete addresses attached to them.

There are various ways to create networks between the soma cores 102. One possibility is to send all data packets from a central starting point to each recipient. From this starting point, data packets can also easily be sent to other soma groups. Advantages of this approach include direct delivery, high throughput (no conflicts with transmissions to different targets), and low latency. One drawback is high cost, especially with one network per soma or per group of somas.

Another approach would be to provide point-to-point connections with a limited set of soma cores 102 and have recipients distribute data packages further. The recipients can be connected to different subsets of the soma cores 102, and these subsets can be selected to ensure that all soma cores 102 are connected. Ideally, the subsets can be selected to reduce or minimize the “diameter” of the network, where the diameter of a network refers to the maximal distance (the number of soma cores 102 to step through to reach a target) between two cores 102. Given a fixed upper limit on the number of connections per soma core 102, a hypercube architecture of that degree could minimize the diameter.

To ensure that all soma cores 102 receive data and spread transmissions over as many individual connections as possible, various approaches could be used. For example, well-known algorithms can take the index of a sender soma core 102 and the link that data was received from into account. In those cases, data from each soma core 102 can be sent in a fixed pattern, but the pattern can be different for individual soma cores 102, maximizing the utilization of connections. This approach also allows elimination of a central starting location for each network since each soma core 102 could just communicate with selected neighbors and the neighbors could forward data if necessary. One or more soma cores 102 in a network could be responsible for sending data to other soma groups, and different soma cores 102 may be responsible for communications with different soma groups.

Dynamic algorithms can also be used. For example, every received packet can be forwarded from one soma core 102 to all neighbors (except the soma core 102 sending the packet). Each neighbor soma core 102 could then keep track of whether it has already seen the packet. If so, the packet can simply be discarded. If not, the synapse coprocessor 112 for the neighbor soma core 102 receives and forwards the packet. One advantage of this approach is that the network can be completely flooded more quickly. Another advantage of this approach is that integrating multiple soma groups into the design is more straightforward. Changing a 1:N bus architecture (which never has to check for sender conflicts) to an S:N architecture can be a big step. If a soma core 102 of one soma group forwards a packet to another soma core 102 in another soma group, the latter can regard the packet similar to how it would regard any other incoming packet. In fact, the inter-soma core link can be regarded like normal inter-soma intra-soma group connections.

As noted above, a number of new instructions can be used to facilitate the use of the synapse coprocessors 112 and the reducers 115. These instructions include instructions executed by the soma cores 102, as well as instructions provided to and executed by the synapse coprocessors 112 and the reducers 115. The following presents examples of the types of new instructions that can be used to support the new hardware architectures. Note that while specific instructions are described below, other or additional instructions could be supported in a hardware architecture as needed or desired.

Table 1 illustrates example instructions that could be executed by a soma core 102 and the synapse coprocessors. In Table 1, oreg denotes a soma core register (such as in the memory device 106), and yreg denotes a synapse coprocessor register (such as in the memory device 114).

TABLE 1 Instruction Description send oreg → channel Broadcast a soma core's value from the oreg register to synapse coprocessors of other soma cores using a specific channel (this could be done in parallel with broadcasts on other channels). recv channel → oreg1 Receive from the local reducer the results of the last [, oreg2] computation in channel. The results are stored in the provided registers. Two results are returned for certain reduction operations which then require two result registers. store oreg → channel Broadcast a soma core's value from the oreg register to all synapse coprocessors of this soma core using a specific channel. synapse channel Receive a value from a specified channel and store it in the { recv → yreg . . . } synapse coprocessor's yreg register. The source of the data [reduce . . . ] can be a ‘send’ or ‘store’ instruction. This event may then trigger further synapse coprocessor instructions. Upon completion, a reduction step optionally happens with the different operations as shown in Table 2. id → oreg Provide a soma core identifier into the oreg register

Table 2 illustrates example operations that could be executed by a reducer 115. Reduction operations could take many cycles logarithmically, so the reduction operations could benefit from pipelining multiple such operations in different tree levels.

TABLE 2 Instruction Description reduce add → oreg Sum all synapse coprocessors' outputs and store the sum in the oreg register. reduce min → oreg1, Identify the minimum value of all synapse coprocessors' oreg2 outputs from their first result and store the minimum value in the oreg1 register. The second result the synapse coprocessor providing the minimum value is stored in the oreg2 register. reduce max → oreg1, Identify the maximum value of all synapse coprocessors' oreg2 outputs from their first result and store the maximum value in the oreg1 register. The second result of the synapse coprocessor providing the maximum value is stored in the oreg2 register. reduce one yreg → oreg Store the value of a specific synapse coprocessor's yreg result for a specific channel in the oreg register.

In some embodiments, each synapse coprocessor 112 can perform SIMD operations. Each soma core 102 can upload, ahead of data communications on a specific channel, sequences of instructions for that channel to a local synapse coprocessor 112. Additionally, each soma core 102 can upload sequences of instructions for that channel to all its synapse coprocessors 112 by broadcasting. The soma core 102 can further program into the reducer 115 the operation that should be performed once the necessary input data becomes available. Table 3 illustrates examples of the types of instructions that could be uploaded to the synapse coprocessors 112 for execution.

TABLE 3 Instruction Description id → yreg Provide a synapse identifier into a synapse coprocessor's yreg register. In case of an implementation with multiple soma groups, the output includes a differentiation of the soma group, as well. add yreg1 yreg2 → Compute a sum of two synapse coprocessor registers yreg1 yreg3 and yreg2 and store a result in yreg3 subtract yreg1 yreg2 → Compute a difference of two synapse coprocessor registers yreg3 yreg1 and yreg2 and store a result in yreg3 multiply yreg1 yreg2 → Compute a product of two synapse coprocessor registers yreg3 yreg1 and yreg2 and store a result in yreg3 min yreg1 yreg2 → Compute a minimum of two synapse coprocessor registers yreg3 yreg1 and yreg2 and store a result in yreg3 max yreg1 yreg2 → Compute a maximum of two synapse coprocessor registers yreg3 yreg1 and yreg2 and store a result in yreg3 invsqrt yreg1 → yreg2 Compute a reciprocal square root of a synapse coprocessor register yreg1 and store a result in yreg2 if yreg1 then yreg2 else Select one of two synapse coprocessor registers yreg2 and yreg3 → yreg4 yreg3 based on yreg1 and store the selected value in yreg4 return yreg1[, yreg2] Pass value(s) yreg1 (and in some cases yreg2) and signal completion to a reducer

The hardware architectures described above can accelerate a broad class of algorithms in machine learning, scientific computing, video games, and other areas. Based on the types of instructions above, the following describes how six example types of problems can be accelerated and solved using the hardware architectures described in this patent document.

As a first example, one algorithm used in deep learning that can be accelerated by the proposed architectures is sparse coding. In its simplest form, sparse coding takes a normalized input vector x with ∥x∥=1 and computes a normalized sparse output vector y that minimizes energy e, which is defined as:

$\begin{matrix} {e = {{\frac{1}{2}{{y - {Fx}}}^{2}} + {\lambda{y}_{\ell^{i}}}}} & (2) \end{matrix}$ Here, F is a factor matrix, and ∥y∥=1. Also, ∥y∥_(l) ₁ denotes a sum of the absolute values of the entries in y, and λ is a constant that controls sparseness of the output. In unsupervised learning mode, the factor matrix F is chosen to minimize the sum E of the energies e_(i) across a set of training inputs x_(i). One way to accomplish both minimizations is gradient descent, with the negative gradients defined as: −∇_(y) _(i) E=−(y _(i) −Fx _(i))+λsgn y _(i)  (3) −∇_(F) E=Σ _(i)(y _(i) −Fx _(i))

x _(i)  (4) followed by imposition of the constraints ∥y_(i)∥=1. Here, sgn y denotes a vector of signs of the entries in y.

To compute (y−Fx), the training inputs x and the outputs y can reside in a shared virtual or local soma memory. The entries of the factor matrix F (which is not sparse) can reside in registers of the synapse coprocessors 112. Specifically, the entry F^(jk) of the factor matrix F can reside in a register of the k^(th) synapse coprocessor 112 for the j^(th) soma core 102. The SIMD instructions broadcast by the soma cores 102 to their synapse coprocessors 112 can use relative addressing so that, simultaneously across soma cores 102, the k^(th) soma core 102 can broadcast the input entry x^(k) to the k^(th) synapse coprocessor 112 of the j^(th) soma core 102. The k^(th) synapse coprocessor of the j^(th) soma core 102 in SIMD fashion performs the multiplication F^(jk)x^(k), which is then summed in logarithmic time by the reducer 115 of the j^(th) soma core 102 across that soma core's synapse coprocessors 112 to yield (Fx)^(j) and thus the j^(th) entry (y−Fx)^(j).

To compute the gradient descent for F, the entry F^(jk) is incremented proportionally to (y−Fx)^(j)x^(k). The j^(th) soma core 102 has just computed (y−Fx)^(j), and its k^(th) synapse coprocessor 112 has received the most recent x^(k) value and stored it in a register of the synapse coprocessor 112. Thus, the j^(th) soma core 102 broadcasts Fx)^(j) to its k^(th) synapse coprocessor 112, which then in SIMD fashion multiplies the result by the stored x^(k) value and adds a multiple of that value to the F^(jk) value stored at that synapse coprocessor 112.

To express this in pseudocode, since the soma cores 102 are multiple instruction, multiple data (MIMD) cores, a convention is adopted where i represents the index of the soma core 102 on which the instruction is being placed. Due to MIMD, the instructions may be parameterized by i. In contrast, since the synapse coprocessors 112 could be SIMD cores, the soma cores 102 can broadcast the same instruction sequence to all of its synapse coprocessors 112. For clarity, registers are labeled with variable names instead of register numbers. Given these conventions, the sparse coding for deep learning problem can be solved using the hardware architecture as follows.

send x →cid1 synapse cid1 {  recv → x  multiply F x → y’  return y’ } reduce add recv cid1 → y’ y − y’→ dy store dy → cid2 synapse cid2 {  recv → dy  multiply dy x → dF  multiply dF −e → dF  add F dF → F }

As a second example, another algorithm used in deep learning that can be accelerated by the proposed architectures involves restricted Boltzmann machines. In this type of network, a {−1,1}-valued input vector x and an output vector y can be probabilistically related by a Boltzmann distribution as follows:

$\begin{matrix} {{P\left( {x,y} \right)} = \frac{e^{- {E{({x,y})}}}}{Z}} & (5) \end{matrix}$ Here, Z is a partition function, and energy E(x,y) in its simplest form can be expressed as: E(x,y)=−Σ_(j,k) y ^(j) F ^(jk) x ^(k)  (6)

This network is “restricted” in the sense that the outputs are conditionally independent given the inputs and vice versa. This means that, given the inputs, the outputs can be sampled independently with a probability expressed as: P(y ^(j)=1|x)=σ(Σ_(k) F ^(jk) x ^(k))  (7) where σ(x) is a logistic function. The contrastive divergence unsupervised training algorithm for this network takes a gradient for a coupling F to be: ∇F=y′

x′−y

x  (8) where x is a training input, y is sampled from x as explained above, x′ is sampled from y, and y′ is sampled from x′.

To implement this problem, the training inputs x^(k) and the outputs y^(j) can reside in a shared virtual or local soma memory. The couplings F^(jk) can reside in registers of the synapse coprocessors 112. Specifically, each coupling P^(k) can reside in a register of the k^(th) synapse coprocessor 112 of the j^(th) soma core 102. To explain how this algorithm is accelerated, the sampling step is first explained. Given an input vector x, via SIMD communication simultaneously across soma cores 102, the k^(th) soma core 102 broadcasts the input entry x^(k) to the k^(th) synapse coprocessor 112 of the j^(th) soma core 102. The k^(th) synapse coprocessor 112 of the j^(th) soma core 102 then in SIMD fashion performs the multiplication F^(jk)x^(k), which is then summed in logarithmic time by the reducer 115 of the j^(th) soma core 102 across that soma core's synapse coprocessors 112 to yield Σ_(k)F^(jk)x^(k). The j^(th) soma core 102 then computes the logistic function of this sum and uses it as a probability to randomly sample y^(j) from {−1,1}.

Next, the computation of the gradient occurs. Starting with the training input x, perform the sampling step as described above three times to yield y in the j^(th) soma core 102, x′ in the k^(th) soma core 102, and y′ in the j^(th) soma core 102. The j^(th) soma core 102 broadcasts y^(i) and (y′)^(j) to all its synapse coprocessors 112 to be stored in registers there. Then, high-bandwidth communication is used to simultaneously transmit (x′)^(k) from the k^(th) soma core 102 to the k^(th) synapse coprocessor 112 of every soma core 102. Finally, the k^(th) synapse coprocessor 112 of the j^(th) soma core 102 calculates

(y′)^(j)(x′)^(k)−y^(j)x^(k) and subtracts a multiple of this from the value j^(ik) that it holds.

In pseudocode, the forward sampling algorithm can be expressed as:

send x → cid synapse cid {  recv → x  multiply F x → y’  return y’ } reduce add recv cid → y’ (σy’) → p if(rand( ) < p) then y = 1 else y = −1 endif The backward sampling can be analogous. Given the sampling, the gradient algorithm can be expressed as:

forward sample x → y (keep x in synapse register) backward sample y → x’ (keep y in synapse register) forward sample x’ → y’ (keep x’ in synapse register) store y’ → cid2 synapse cid2 {  recv → y’  multiply y’ x’ → yx’  multiply y x −1 → yx  add yx’ yx → dF  multiply dF −e → dF  add F dF → F }

As a third example, a different machine learning method that can benefit from better communication is hierarchical clustering. The simplest hierarchical clustering method starts with each item in its own cluster. Then, at each hierarchy level, the hierarchical clustering method groups the two clusters separated by the smallest minimum distance into a single cluster.

The first step of an improved hierarchical clustering method involves calculating an initial matrix of distances between clusters. Each active soma core 102 can represent a cluster, and its synapses coprocessors 112 can store the squared distances to other clusters. In a first iteration, each cluster is a single item, so each active soma core 102 broadcasts its item's coordinates to the corresponding synapse coprocessors 112 of the other soma cores 102, and its synapse coprocessors 112 in parallel compute the squared distances of the other items to its own item. The second step of the improved hierarchical clustering method involves finding the minimum squared distance between clusters. Each soma core 102 (through its reducer 115) reduces its own synapse coprocessors' squared distances using the minimum operation, and each soma core 102 broadcasts this number to all soma cores 102, which again reduce the values (through their reducers 115) with a minimum operation. The second minimum operation produces on all soma cores 102 the same result, assuming there is a predictable tie breaker in cases of equal values (such as select the lowest index synapse coprocessor's value). An alternative is to perform the second minimum operation on one soma core 102 and broadcast back the result to all other soma cores 102.

The third step of the improved hierarchical clustering method involves finding the two clusters that are separated by this minimum distance. The soma core 102 corresponding to the best cluster computes the minimum distance to a soma core 102 other than itself, and this next best cluster is then broadcast back to all soma cores 102. The fourth step of the improved hierarchical clustering method involves combining the two chosen clusters into a single cluster. Each soma core 102 takes the minimum of its distances to the best and next best clusters, stores the minimum distance hack in the synapse coprocessor 112 corresponding to the best cluster, and broadcasts the minimum distance on this soma core's channel. The soma core 102 corresponding to the best cluster then has all of its synapse coprocessors 112 replace their distances with these broadcast ones. Finally, the next best soma core 102 and its corresponding synapse coprocessors 112 drop out of the computation. The second through fourth steps are then repeated until there is only a single cluster.

In pseudocode, the first step of calculating the squared distance matrix (repeating for each coordinate′ can be expressed as:

send −x → cid synapse cid {  recv → x’  add x x’ → dx // x is the local cluster’s coordinate  multiply dx dx → dx  add dist dx → dist  return dist } reduce min recv cid → mindist

The second step of finding the minimum distance between clusters can be expressed as:

send mindist → cid2 synapse cid2 {  recv → mindist ; id → cluster  return mindist, cluster } reduce min recv cid2 → allmindst, mincluster

The third step of finding the two clusters separated by the minimum distance can be expressed as:

if(mincluster == id) then  store −mincluster → cid3  synapse cid3 {   recv → mincluster   id → cluster   add cluster mincluster → notmin   if notmin then dist else ∞ → mindist   return mindist, cluster  } reduce min  recv cid3 → dummy, nextcluster  send nextcluster → cid4 else  send 0 → cid4 endif synapse id {  recv → nextcluster } reduce one mincluster recv cid5 → nextcluster store −mincluster → cid6 synapse cid6 {  recv → mincluster  id → cluster  add cluster mincluster → notmin  return dist } reduce one mincluster recv cid6 → mindist store −nextcluster → cid7 synapse cid7 {  recv → nextcluster  add cluster nextcluster → notnext  return dist } reduce one nextcluster recv cid7 → nextdist mindist = min(mindist, nextdist)

The fourth step of combining the two closest clusters (and deactivating one of them) can be expressed as:

store mindist → cid8 synapse cid8 {  recv → mindist  if notmin then dist else mindist → dist  if notnext then dist else ∞ → dist } send mindist → cid9 if(mincluster == id) then  synapse cid9 { recv → dist } elif(nextcluster == id) then  synapse cid9 { recv → dummy; ∞ → dist } else  synapse cid9 { recv → dummy } endif

As a fourth example, another popular machine learning method involves Bayesian networks, which decompose a complicated joint probability function of many variables into a product of conditional probabilities, each of which involves only a small number of variables (up to the in-degree of the network). The problem then is to compute the marginal distribution of each variable. In a standard serial architecture, this can be accomplished using the Belief Propagation Algorithm, which takes time proportional to: Variables×In-Degree×2^(In-Degree)  (9) This algorithm iteratively computes the above number of products and then computes Variables×In-Degree sums of 2^(In-Degree) such products each.

Using the new hardware architectures, this can be accomplished in constant time as long as there are adequate soma cores 102 and synapse coprocessors 112. The fan-in to any one soma core 102 is only 2^(In-Degree), so this does not saturate communications. To compute products, one can either accumulate sums of logs (where the exp and log operations are performed in the soma cores 102) or expand the available accumulation methods of the reducer 115 to include products as well as sums.

As a fifth example, other applications unrelated to artificial intelligence that could be accelerated with the architectures include molecular simulation and virtual reality. For these applications, assume that the synapse coprocessors 112 have hardware for a reciprocal square root operation (1/√{square root over (x)}) in addition to multiplication and addition. The expensive step in both applications is similar. Focusing on molecular simulation, it is the computation of the Coulomb potential:

$\begin{matrix} {U_{j} = {\sum_{k \neq j}\frac{q_{j}q_{k}}{r_{jk}}}} & (10) \end{matrix}$ where q_(j) is the j^(th) charge and r_(jk) is the distance between the j^(th) and k^(yth) charges. High-bandwidth communication takes care of simultaneously broadcasting the coordinates of the k^(th) charge from the r soma core 102 to the k^(th) synapse coprocessor of the j^(th) soma core 102 across all j and k. In each synapse coprocessor 112, addition and multiplication are used to compute r_(jk) ² and then the reciprocal square root is used to compute 1/r_(jk). Finally, the sum is computed by the j^(th) soma core 102 using an accumulator (the reducer 115) across its synapse coprocessors 112.

As a sixth example, another class of algorithms that can be accelerated from quadratic to constant time by the proposed architectures involves geometric algorithms, such as convex hull algorithms. These algorithms may not require the nonlinear capabilities of the proposed architectures and may only rely on the matrix processing capabilities of the proposed architectures. It shown been shown that one key step of these algorithms in high dimensions is dynamic determinant computation. This computation can be accomplished serially in quadratic time by matrix-vector multiplications. However, these multiplications can be reduced to constant time using the proposed architectures.

Note that these examples are provided above merely to demonstrate how particular solutions to particular problems could be solved using the hardware architectures described in this patent document. Of course, the hardware architectures could be used to perform other functions. Moreover, the particular problems described above could be solved using other solutions implemented using the hardware architectures.

The hardware architectures and associated instructions/operations described in this patent document can provide various advantages over prior approaches, depending on the implementation. For example, this disclosure provides hardware architectures that (if implemented with an adequate number of components) allow the architectures to rival the abilities of the human brain. Moreover, the functionalities of the hardware architectures can be used to improve other fields of computing, such as artificial intelligence, deep learning, molecular simulation, and virtual reality.

In some embodiments, various functions described in this patent document are implemented or supported by a computer program that is formed from computer readable program code and that is embodied in a computer readable medium. The phrase “computer readable program code” includes any type of computer code, including source code, object code, and executable code. The phrase “computer readable medium” includes any type of medium capable of being accessed by a computer, such as read only memory (ROM), random access memory (RAM), a hard disk drive, a compact disc (CD), a digital video disc (DVD), or any other type of memory. A “non-transitory” computer readable medium excludes wired, wireless, optical, or other communication links that transport transitory electrical or other signals. A non-transitory computer readable medium includes media where data can be permanently stored and media where data can be stored and later overwritten, such as a rewritable optical disc or an erasable memory device.

It may be advantageous to set forth definitions of certain words and phrases used throughout this patent document. The terms “application” and “program” refer to one or more computer programs, software components, sets of instructions, procedures, functions, objects, classes, instances, related data, or a portion thereof adapted for implementation in a suitable computer code (including source code, object code, or executable code). The term “communicate,” as well as derivatives thereof, encompasses both direct and indirect communication. The terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation. The term “or” is inclusive, meaning and/or. The phrase “associated with,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, have a relationship to or with, or the like. The phrase “at least one of,” when used with a list of items, means that different combinations of one or more of the listed items may be used, and only one item in the list may be needed. For example, “at least one of A, B, and C” includes any of the following combinations: A, B, C, A and B, A and C, B and C, and A and B and C.

The description in this patent document should not be read as implying that any particular element, step, or function is an essential or critical element that must be included in the claim scope. Also, none of the claims is intended to invoke 35 U.S.C. § 112(f) with respect to any of the appended claims or claim elements unless the exact words “means for” or “step for” are explicitly used in the particular claim, followed by a participle phrase identifying a function. Use of terms such as (but not limited to) “mechanism,” “module,” “device,” “unit,” “component,” “element,” “member,” “apparatus,” “machine,” “system,” “processor,” “processing device,” or “controller” within a claim is understood and intended to refer to structures known to those skilled in the relevant art, as further modified or enhanced by the features of the claims themselves, and is not intended to invoke 35 U.S.C. § 112(f).

While this disclosure has described certain embodiments and generally associated methods, alterations and permutations of these embodiments and methods will be apparent to those skilled in the art. Accordingly, the above description of example embodiments does not define or constrain this disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure, as defined by the following claims. 

What is claimed is:
 1. An apparatus comprising: multiple computing cores, each computing core configured to perform one or more processing operations and generate input data; multiple sets of coprocessors each uniquely associated with a different one of the computing cores, each coprocessor configured to receive the input data from at least one of the computing cores, process the input data, and generate output data; multiple reducer circuits each uniquely associated with a different one of the computing cores, each reducer circuit configured to receive the output data from the coprocessors in the set of coprocessors associated with one of the computing core uniquely associated with the reducer circuit, apply one or more functions to the output data, and provide one or more results to the computing core uniquely associated with the reducer circuit; and multiple communication links communicatively coupling the computing cores and at least some of the coprocessors.
 2. The apparatus of claim 1, wherein the communication links comprise direct connections between the computing cores and at least some of the coprocessors.
 3. The apparatus of claim 1, wherein the communication links comprise one or more direct connections between at least one of the computing cores and one or more coprocessors at a beginning of one or more chains of coprocessors.
 4. The apparatus of claim 1, wherein: the communication links comprise a direct connection between one of the computing cores and one of the coprocessors; and the one of the coprocessors is coupled to multiple additional ones of the coprocessors.
 5. The apparatus of claim 1, wherein at least some of the coprocessors are arranged in at least one tree.
 6. The apparatus of claim 1, wherein the communication links comprise links to a shared resource, the shared resource configured to store the input data from the computing cores and to provide the input data to the coprocessors.
 7. The apparatus of claim 6, wherein the shared resource comprises a shared memory.
 8. The apparatus of claim 7, wherein: the shared memory comprises multiple memory locations having multiple memory addresses; the computing cores are configured to write the input data to different memory addresses; and the coprocessors are configured to read the input data from the different memory addresses.
 9. An apparatus comprising: multiple computing cores, each computing core configured to perform one or more processing operations and generate input data; multiple sets of coprocessors each uniquely associated with a different one of the computing cores, each coprocessor configured to receive the input data from at least one of the computing cores, process the input data, and generate output data; and multiple communication links communicatively coupling the computing cores and at least some of the coprocessors; wherein a subset of the coprocessors in each set of coprocessors is also configured to collectively apply one or more functions to the output data generated by the coprocessors in that set of coprocessors, one of the coprocessors in each set of coprocessors further configured to provide one or more results to the computing core uniquely associated with that set of coprocessors.
 10. The apparatus of claim 9, wherein the communication links comprise direct connections between the computing cores and at least some of the coprocessors.
 11. The apparatus of claim 9, wherein the communication links comprise one or more direct connections between at least one of the computing cores and one or more coprocessors at a beginning of one or more chains of coprocessors.
 12. The apparatus of claim 9, wherein: the communication links comprise a direct connection between one of the computing cores and one of the coprocessors; and the one of the coprocessors is coupled to multiple additional ones of the coprocessors.
 13. The apparatus of claim 9, wherein at least some of the coprocessors are arranged in at least one tree.
 14. The apparatus of claim 9, wherein the communication links comprise links to a shared resource, the shared resource configured to store the input data from the computing cores and to provide the input data to the coprocessors.
 15. The apparatus of claim 14, wherein the shared resource comprises a shared memory.
 16. The apparatus of claim 15, wherein: the shared memory comprises multiple memory locations having multiple memory addresses; the computing cores are configured to write the input data to different memory addresses; and the coprocessors are configured to read the input data from the different memory addresses.
 17. An apparatus comprising: N parallel computing cores, each computing core configured to perform one or more processing operations and generate input data; N×N coprocessors, wherein each computing core is associated with N distinct parallel coprocessors, each coprocessor configured to receive the input data from at least one of the computing cores, process the input data, and generate output data; N reducer circuits, each computing core associated with a distinct one of the reducer circuits, each reducer circuit configured to receive the output data from the N coprocessors of the computing core distinctly associated with the reducer circuit, apply one or more functions to the output data, and provide one or more results to the computing core distinctly associated with the reducer circuit; and multiple communication links communicatively coupling the computing cores and at least some of the coprocessors.
 18. The apparatus of claim 17, wherein N is an integer having a value of at least sixteen.
 19. The apparatus of claim 17, wherein the communication links comprise links to a shared resource, the shared resource configured to store the input data from the computing cores and to provide the input data to the coprocessors.
 20. The apparatus of claim 19, wherein: the shared resource comprises a shared memory; the shared memory comprises multiple memory locations having multiple memory addresses; the computing cores are configured to write the input data to different memory addresses; and the coprocessors are configured to read the input data from the different memory addresses. 